U.S. Rep. Cathy McMorris Rodgers, R-Wash., a member of Republican House leadership, back Special Counsel Robert Mueller's probe of Russia's interference in the 2016 election. She also leave open prospect of impeaching Deputy Attorney General Rod, who is overseeing the probe.

U.S. Rep. Cathy McMorris Rodgers, R-Wash., a member of Republican House leadership, back Special Counsel Robert Mueller's probe of Russia's interference in the 2016 election. She also leave open prospect of

Deputy Attorney General Rod Rosenstein, left, speaks as U.S. Attorney Annette L. Hayes looks on. Rosenstein is on the hot seat as overseer of the Russiaprobe by Special Counsel Robert Mueller III. Such Trump loyalists as House Intelligence Committee Chairman Devin Nunes want him fired. Rep. Cathy McMorris Rodgers, R-Wash. is open to the possibility. (AP Photo/Elaine Thompson)

Deputy Attorney General Rod Rosenstein, left, speaks as U.S. Attorney Annette L. Hayes looks on. Rosenstein is on the hot seat as overseer of the Russiaprobe by Special Counsel Robert Mueller III. Such

But McMorris Rodgers hinted that a Republican-run House could still take up impeachment of Deputy Attorney General Rod Rosenstein, who is overseeing the Russia investigation by Special Counsel Robert Mueller III.

McMorris Rodgers is doing a straddling act, between Republicans who accept President Trump's charge that the Russia probe is a "witch hunt" and the majority of Americans who tell pollsters they want to see out the investigation.

The Eastern Washington lawmaker has been in the vortex of a national news story. She held a closed fundraiser on July 30 with Rep. Devin Nunes, R-Calif., chairman of the House Intelligence Committee and a vociferous Trump supporter.

A tape of the luncheon leaked out and was first broadcast on MSNBC. At the Spokane Club event, Nunes said Republicans need to keep control of the House in order to protect President Trump.

McMorris Rodgers, a member of the House Republican leadership, has been the public face of Trump administration policies in Washington state. She backed Trump in Washington's 2016 Republican presidential primary.

"I've said repeatedly that I support the independent investigation into allegations about Russian involvement in the 2016 election," she said in a statement. "The Special Counsel should complete its work as soon as possible and be transparent to the American people."

(The Mueller investigation has released no information other than its indictments of such personages as 2016 Trump campaign manager Paul Manafort.)

At the same time, McMorris Rodgers backed demands for information by House Republicans directed at the Department of Justice. Attacks on the DOJ and Rosenstein have come from Nunes and other Trump defenders.

"It's also critical that the American people are able to trust the Department of Justice, our nation's top law enforcement agency," added McMorris Rodgers. "To that end, the Department of Justice and Rod Rosenstein need to make a better effort to turn over the documents that Congress has requested -- and I expect them to do so and fully comply with appropriate congressional oversight."

Or else!

"If they don't," said McMorris Rodgers, "then Congress should follow regular order to determine if impeachment is the best path forward to restore the public's trust in the nation's top law enforcement agency."

The chief effort to undermine that trust have come in tweets from President Trump. He has belittled Attorney General Jeff Sessions and attacking Sessions' decision to recuse himself from the Russia probe. The President has made equally unpleasant remarks about Rosenstein.

At the fundraiser, Nunes said Republicans have to keep their House majority in order to protect Trump.

"If Sessions won't unrecuse and Mueller won't clear the President, we're the only ones," said the committee chair.

"I mean, we have to keep all these seats. We have to keep the majority. If we do not keep the majority, all this goes away."

McMorris Rodgers is in danger of being unseated. She ran even on primary election night with Democratic challenger Lisa Brown, until recently chancellor of Washington State University-Spokane.

SeattlePI.com columnist/blogger Joel Connelly can be reached at Joel Connelly@seattlepi.com

Columnist Joel Connelly has written about politics for the P-I since 1973.